Electromagnetic exploration

ABSTRACT

A system and method include receiving electromagnetic energy emanating from a target using a plurality of receivers, and generating a pseudo-source based at least in part on a location of one or more of the plurality of receivers and the received electromagnetic information.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims priority to Provisional U.S. Patent ApplicationSer. No. 61/057,606, filed May 30, 2008, which is hereby incorporated byreference in its entirety.

TECHNICAL FIELD

The present disclosure generally relates to electromagnetic surveyingand in particular to methods and apparatus for acquiring and processinggeophysical information.

BACKGROUND

In the oil and gas exploration industry, geophysical tools andtechniques are commonly employed in order to identify a subterraneanstructure having potential hydrocarbon deposits. One such techniqueutilizes electromagnetic energy in a process known as electromagneticprospecting.

Electromagnetic prospecting is a geophysical method employing thegeneration of electromagnetic fields at the Earth's surface. Theelectromagnetic fields may have a wave character, a diffusive character,or a combination of the two. When the fields penetrate the Earth andimpinge on a conducting formation or orebody, they induce currents inthe conductors, which are the source of new fields radiated from theconductors and detected by instruments at the surface.

SUMMARY

The following presents a general summary of several aspects of thedisclosure in order to provide a basic understanding of at least someaspects of the disclosure. This summary is not an extensive overview ofthe disclosure. It is not intended to identify key or critical elementsof the disclosure or to delineate the scope of the claims. The followingsummary merely presents some concepts of the disclosure in a generalform as a prelude to the more detailed description that follows.

Disclosed is a method for gathering geophysical information thatincludes receiving electromagnetic energy emanating from a subsurfacetarget using a plurality of receivers, and generating a pseudo-sourcebased at least in part on a location of one or more of the plurality ofreceivers and the received electromagnetic information.

BRIEF DESCRIPTION OF THE DRAWINGS

For a detailed understanding of the present disclosure, reference shouldbe made to the following detailed description of the severalnon-limiting embodiments, taken in conjunction with the accompanyingdrawings, in which like elements have been given like numerals andwherein:

FIG. 1 is a non-limiting example of a geophysical information gatheringsystem;

FIG. 2 illustrates a non-limiting example of sensor nodes that may beused according to several embodiments of the disclosure;

FIG. 3 illustrates several non-limiting examples of an electromagneticradiator that may be used in a system according to FIG. 1;

FIGS. 4, 5 and 6 illustrate electric field diagrams associated with acube-like electromagnetic source;

FIGS. 7, 8 and 9 illustrate magnetic field diagrams associated with acube-like electromagnetic source;

FIGS. 10, 11 and 12 illustrate several non-limiting multi-componentsource configurations according to several embodiments of thedisclosure;

FIG. 13 illustrates a non-limiting example of a geophysical informationprocessing system that may be used in accordance with the severalembodiments;

FIG. 14 shows a non-limiting method for geophysical informationprocessing; and

FIG. 15 shows another non-limiting method for geophysical informationprocessing.

DESCRIPTION OF EXEMPLARY EMBODIMENTS

Portions of the present disclosure, detailed description and claims maybe presented in terms of logic, software or software implemented aspectstypically encoded on a variety of media including, but not limited to,computer-readable media, machine-readable media, program storage mediaor computer program product. Such media may be handled, read, sensedand/or interpreted by an information processing device. Those skilled inthe art will appreciate that such media may take various forms such ascards, tapes, magnetic disks (e.g., floppy disk or hard drive) andoptical disks (e.g., compact disk read only memory (“CD-ROM”) or digitalversatile (or video) disc (“DVD”)). Any embodiment disclosed herein isfor illustration only and not by way of limiting the scope of thedisclosure or claims.

The present disclosure uses terms, the meaning of which terms will aidin providing an understanding of the discussion herein. For example, theterm information processing device mentioned above as used herein meansany device that transmits, receives, manipulates, converts, calculates,modulates, transposes, carries, stores or otherwise utilizesinformation. In several non-limiting aspects of the disclosure, aninformation processing device includes a computer that executesprogrammed instructions for performing various methods.

Geophysical information as used herein means information relating to thelocation, shape, extent, depth, content, type, properties of and/ornumber of geologic bodies. Geophysical information includes, but is notnecessarily limited to marine and land electromagnetic information.Electromagnetic information as used herein includes, but are not limitedto, one or more or any combination of analog signals, digital signals,recorded data, data structures, database information, parametersrelating to surface geology, source type, source location, receiverlocation, receiver type, time of source activation, source duration,source frequency, energy amplitude, energy phase, energy frequency, waveacceleration, wave velocity and/or wave direction, field intensityand/or field direction.

Geophysical information may be used for many purposes. In some cases,geophysical information may be used to generate an image of subterraneanstructures. Imaging, as used herein includes any representation of asubsurface structure including, but not limited to, graphicalrepresentations, mathematical or numerical representation, strip chartsor any other process output representative of the subsurface structure.

FIG. 1 is a non-limiting example of a geophysical information gatheringsystem 100. The system 100 may include any number of subsystems andcomponents. The system 100 in this example includes an energy source102. One or more sensors 104 are positioned in a survey area, and thesensors are coupled to a recorder 106. In one or more embodiments, thesensors 104 may be incorporated into an ocean-bottom cable 118 and theocean-bottom cable may be connected to the recorder 106 via a suitablecommunication interface 120, such as a riser cable. In this example, theocean-bottom cable is shown position in or on the seabed 122 wheresignals emanating from a target 124, which may include subterraneanstrata, a hydrocarbon-bearing reservoir or other geologic structure, maybe detected by the several sensors 104. The non-limiting system 100illustrates a marine environment and a radiator 110 being towed by avessel 112. In other embodiments, a radiator may be towed in an airborneconfiguration over a body of water or over land without departing fromthe scope of the disclosure. In other embodiments, the electromagneticsource 102 may be deployed in a stationary or semi-stationary fashion onland or in a marine environment without departing from the scope of thedisclosure. Regardless of the environment selected for the geophysicalinformation gathering system 100, the information gathered may beprocessed according to several methods disclosed herein by using asuitable geophysical information processing system.

The sensors 104 may include any number of sensors useful in gatheringgeophysical information. In one or more embodiments, the sensors mayinclude electromagnetic sensors such as antennas, electrodes,magnetometers or any combination thereof. In one or more embodiments,the sensors may include pressure sensors such as microphones,hydrophones and their combinations. In one or more embodiments, thesensors 104 may include particle motion sensors such as geophones,accelerometers and combinations thereof. In one or more embodiments, thesensors may include combinations of electromagnetic sensors, pressuresensors and particle motion sensors. The non-limiting example system ofFIG. 1 illustrates a sensor arrangement using an ocean-bottom cable 118.In one or more embodiments, sensor stations may be placed on the seabedand received signals may be recorded at each sensor station.

FIG. 2 illustrates a non-limiting example of sensor nodes that may beused according to several embodiments of the disclosure. Shown are twosensor nodes 200 that may be substantially similar to one another. Eachsensor node 200 is placed on the seabed 122, although land deployment iswithin the scope of the disclosure. A sensor node 200 according to oneor more embodiments may include several faces 202. Each face may includean electric field sensor 204 and a magnetic field sensor 206. Thesensors 204, 206 may be in the form of dipole antennas. In the exampleembodiment of FIG. 2, the nodes 200 are stand-alone, and do not use acable 118 or surface recorder 106 as in the example system describedabove and shown FIG. 1. The nodes 200, however, may be modified forconnecting to a cable and remote recorder without departing from thescope of this disclosure. Each node 200 may include one or morebatteries 208 for providing power to the node 200. In one or moreembodiments, the node 200 may include a memory 210 for storinginformation received at the node 200. A processor 212 may be includedfor controlling the node 200 and for processing information received bythe node 200.

Referring still to FIGS. 1 and 2, the sensors 104, 204, 206 may generateanalog, digital or a combination of analog and digital signals forrecording. The recorder 106 or station 200 may be any suitable recorderfor receiving and storing the signals generated by the sensors 104, 204,206. The recorder 106 or station 200 may include any number ofgeophysical information processing, storing and transmitting components.More detail of at least some components suitable for portions of therecorder 106 or station will be provided later with reference to FIG.13.

The energy source 102 may include any one or combination of severalsource types. In this example, the energy source includes an energygenerator 108 that produces electromagnetic energy useful in a processknown as controlled source electromagnetics (CSEM). The energy generator108 is coupled to a multi-dimensional electromagnetic energy radiator110. The term radiator is used herein to mean any device, structure,mechanism, combination thereof, and subcomponents thereof suitable forradiating energy. In the example system 100 of FIG. 1, the generator 108is shown disposed on a marine vessel 112. The generator 108 may beconfigured for generating alternating current (AC) or direct current(DC) in the radiator 110. When alternating current is used, thefrequency used may be a varying frequency useful in frequency-modulatedCSEM. In one or more embodiments, the amplitude of the current 126flowing in the radiator 110 may be modulated. The radiator 110 iscoupled to the vessel 112 via a suitable coupling 114 and a tow cable116 so that the vessel 112 may convey the radiator 110 through thedesired media. In this example, the radiator 110 is conveyed throughwater at a predefined depth. In one or more embodiments, the tow cable116 and the coupling 114 include a large gauge conductor for carryingelectrical current to the radiator 110. The radiator 110 may be asubstantially straight or curved structure such as a cable, or theradiator 110 may include a multi-dimensional structure.

FIG. 3 illustrates several non-limiting examples suitable formulti-dimensional radiator structures. A multi-dimensional radiatorstructure may include a two-dimensional polygonal structure such as asquare, a triangle, or the like. Orientation of the radiator structuremay vary during operation, and the methods to be described below may beused without precise knowledge of the radiator structure orientation.For example, the radiator structure may be oriented during operationvertically as illustrated in FIG. 1 or horizontally as illustrated inFIG. 3 at 300 and 304, or the radiator structure may be in any otherorientation. The radiator structures shown in FIG. 3 are but a fewexamples that do not limit the disclosure to any particular shape. Thenon-limiting radiator structures shown here include a squaretwo-dimensional radiator structure 300 and a triangular two dimensionalradiator structure 304. Each of these two-dimensional radiatorstructures may be coupled to the vessel 112 via the coupling 114 and towcable 116 as described above and shown in FIG. 1.

Other suitable radiator structures may include three-dimensionalstructures. For example, a cube structure 306 or a tetrahedron radiatorstructure 308 may be coupled to the vessel 112. In some cases, thetowing configuration may be such that the tow cable 116 may be connecteddirectly to a radiator structure as shown with the tetrahedron radiatorstructure 306.

While substantially straight-ribbed radiator structures are shown,curved structures and radiator structures having a combination of curvedand straight-ribbed structures may be used. In one or more embodiments,curved portions of a radiator structure may include at least a portionof curved shapes. Non-limiting examples include a curved structure suchas a circle, oval or the like. Each branch of the multi-dimensionalradiator structure 300, 304, 306, and 308 may carry electrical current126 in a selected circuitous direction. Those skilled in the art withthe benefit of the present disclosure will appreciate that the severalcircuitous current paths will generate both electrical fields andmagnetic fields, each having multiple respective components depending onthe particular current path selected.

FIGS. 4, 5 and 6 illustrate electric field diagrams associated with acube-like electromagnetic dipole-tensor source as an example ofmulti-component electric and magnetic field generating according toseveral embodiments of the disclosure. Those skilled in the art with thebenefit of the present disclosure will be able to extend the teaching ofthe cube-like source to the several other source geometries disclosedherein and to others.

FIG. 4 illustrates that an electric field Ex as indicated at 400 may begenerated in the x-direction by flowing an electrical current i inconductors parallel to the x-direction and in the direction of Ex. FIG.5 illustrates that an electric field Ey as indicated at 500 may begenerated in the y-direction by flowing an electrical current i inconductors parallel to the y-direction and in the direction of Ey. FIG.6 illustrates that an electric field Ez as indicated at 600 may begenerated in the z-direction by flowing an electrical current i inconductors parallel to the z-direction and in the direction of Ez.

FIGS. 7, 8 and 9 illustrate magnetic field diagrams associated with acube-like electromagnetic dipole-tensor source. FIG. 7 illustrates thata magnetic field Hx as indicated at 700 may be generated in thex-direction by flowing an electrical current i in conductors lyingperpendicular to the x-direction. The direction of Hx (or —Hx) may bedetermined by the well-known right-hand rule and the direction ofcurrent flow. Hx is generally a vector perpendicular to a planeassociated with the conductor carrying the current i. Similarly, FIGS. 8and 9 illustrate respective magnetic fields Hy 800 and Hz 900 for acube-like structure.

FIGS. 10, 11 and 12 illustrate several non-limiting multi-componentsource configurations according to several embodiments of thedisclosure. FIG. 10 illustrates a source structure 1000 that may be usedto generate a three-component magnetic field. FIG. 11 illustrates anon-limiting example of a source structure 1100 that may be used togenerate a three-component electric field. FIG. 12 illustrates anon-limiting example of a source structure 1200 that may be used togenerate three-component magnetic fields and three-component electricfields. In one or more embodiments, the angle between any two branchesof the structure 1200 is about 60°.

FIG. 13 illustrates a non-limiting example of a geophysical informationprocessing system 1300 that may be used in accordance with the severalembodiments. Geophysical information may be gathered from a system 100as described above and shown in FIG. 1. In several non-limitingexamples, the system 100 may include one or more or any combination ofthe components shown in FIG. 13. In one example, the system 1300 mayinclude one or more processing devices such as a computer and a storagedevice 1302. The computer may be selected from any number of usefulcomputer devices, examples of which include, but are not limited to,laptop computers 1304, desk top computers 1306, mainframes 1308 and thelike. While a laptop-type is shown, the processing unit need not includeuser interface devices. However, when appropriate, the computer 1304 mayinclude a display, keyboard and or other input/output devices such asprinters/plotters, a mouse, touch screen, audio output and input or anyother suitable user interface.

The computer 1304 may be in communication with the storage device 1302via any known interface and an interface for entering information intothe computer 1304, 1306, 1308 may be any acceptable interface. Forexample, the interface may include the use of a network interface 1310.

The storage device 1302 according to one or more embodiments may be anyuseful storage device having a computer-readable media. Instructions forcarrying out methods that will be described later may be stored oncomputer-readable media in the computer 1304, 1306, 1308 or may bestored on an external storage device 1302.

Operation of the exemplary geophysical information gathering system 100will now be explained with reference to FIGS. 1-13. An electromagneticfield signal may be emanated from the energy source 102 and propagatetoward the seabed 122. The electromagnetic field signal may includeelectric field having one or more electric field components, a magneticfield having one or more magnetic field components or a combination ofelectric and magnetic fields. The electromagnetic field signal travelswithin the earth, and may interact with the subterranean target 124.Conductive targets such as strata, or strata having conductive fluids,will respond to the electromagnetic field signal to generate a responsefield that travels generally upward toward the seabed and sensors 104.The sensors detect the down-going and up-going fields, and the detectedfields are transmitted to the recorder 106 via conductors in thecommunication interface 120.

The recorded signals may be processed on location or may be transmittedto a processing facility having a geophysical information processingsystem 1300 as described above and shown in FIG. 13. The severalprocessing components need not be co-located and may communicate via thenetwork 1310. The methods described herein are based on novelinterferometry concepts that warrant discussion here.

Introduction—Representation theorems in perturbed media

Let the general frequency-domain matrix-vector differential equation,{circumflex over (Ā)}{circumflex over (()}î{circumflex over(ω)}{circumflex over (Ā(iω +v·∇)û+{circumflex over (B)}û+{circumflexover (D)}_(r)û=ŝ, which describes different physical phenomena such asfield propagation (e.g., electromagnetic), diffusive and advectivetransport. û=û(r,ω) is the vector that contains field quantities as afunction of space r and frequency ω. ŝ=ŝ(r,ω) is the source vector. Thematrices Â and {circumflex over (B)} describe spatially-varying mediumparameters. The operator {circumflex over (D)}_(r) contains the spatialdifferential operators ∂_(1,2,3). The term, (iω+v·∇) contains a timederivative (i.e. the Fourier dual of iω) in the medium's referenceframe, and v which is the spatially-varying velocity of the movingmedium.

Theorems for dynamic systems satisfying the linear partial differentialequation above include,

∫_(v) [û _(A) ^(T) Kŝ _(B) −ŝ _(A) ^(T) Kû _(B) ]d ³ r=

û _(A) ^(T) {circumflex over (M)} ₁ û _(B) d ² r+∫ _(v) û _(A) ^(T){circumflex over (M)} ₂ û _(B) d ³ r  (1)

with {circumflex over (M)}₁=K[N_(r)−Â_(A)(v_(A)·n)] and

{circumflex over (M)} ₂ =K[Â _(B)(iω+v _(B)·∇)−Â _(A)(iω−v_(A)·∇)]+K[{circumflex over (B)} _(B) −{circumflex over (B)} _(A)]; and∫_(v) [û _(A) ^(†) ŝ _(B) +ŝ _(A) ⁵⁵⁴ û _(B) ]d ³ r=

û _(A) ^(†) {circumflex over (M)} ₃ û _(B) d ² r+∫ _(v) û _(A) ^(†){circumflex over (M)} ₄ û _(B) d ³ r,  (2)

where {circumflex over (M)}₃N_(r)−Â_(A) ^(†)(v_(A)·n), and {circumflexover (M)}₄=Â_(B)(iω+v_(B)·∇)−Â_(A) ^(†)(iω+v_(A)·∇)+{circumflex over(B)}_(B)+{circumflex over (B)}_(A) ^(†). The subscripts A and B pertainto two wave states, to which we shall refer respectively as State A andState B. The matrix K is a real-valued diagonal matrix K=K⁻¹ such thatKAK=A^(T), KBK=B^(T) and KD_(r)K=−D_(r) ^(T). The superscript T denotesthe transpose, while † represents the adjoint (i.e., theconjugate-transpose matrix). n is the outward-pointing normal at ∂v. Theoperator N_(r) is defined analogously to D_(r) but instead it containsthe n_(i) elements of the vector n.

Equation 1 is a convolution-type reciprocity theorem while equation 2 isa correlation-type theorem. When the field response is described byGreen's tensors (see below), equation 1 results in a generalizedsource-receiver reciprocity theorem when Â_(A)=Â_(B), {circumflex over(B)}_(A)={circumflex over (B)}_(B) and v_(A)=−v_(B). In special casesfor the material properties, the correlation-type theorem in equation 2leads to a general form of Green's function retrieval bycross-correlations (i.e., a general form of interferometry).

Equations 1 and 2 may be rewritten for the special case of perturbedmedia. Physical phenomena in perturbed media can be described by the setof equations

Â(iω+v·∇)û+{circumflex over (B)}û+{circumflex over (D)} _(r) û=ŝÂ ₀(iω+v₀·∇)û ₀ +{circumflex over (B)} ₀ û ₀ +{circumflex over (D)} _(r) û ₀=ŝ  (3)

where the subscript 0 denotes unperturbed field quantities and mediumparameters, whereas its absence indicates field quantities and mediumparameters that are perturbed. Every perturbed quantity or parameter canbe written as a superposition of its unperturbed counterpart and aperturbation. Thus, Â=Â₀+Â_(S), {circumflex over (B)}={circumflex over(B)}₀+{circumflex over (B)}_(S), v=v₀+v_(S) and û=û₀+û_(S), where thesubscript S represents a perturbation. Note that to treat perturbedmedia, the source vector ŝ is the same for both the unperturbed andperturbed cases (equation 3). Subtracting the second in equation 3 fromthe first one yields the identity

{circumflex over (V)}û₀={circumflex over (L)}û_(S);  (4)

where {circumflex over (L)} is the linear differential operator in thefirst line of equation 3, and {circumflex over (V)} is a perturbationoperator given by {circumflex over ( V=Â(iω+v·∇)−{circumflex over(Ā₀(iω+v₀·∇) +{circumflex over (B)}−{circumflex over (B)}₀. Thisoperator is also referred to as the scattering potential in quantummechanics. The identity in equation 4 shows that the field perturbationsû_(S) ⁻ do not satisfy the same field equations as the ones satisfied byfield quantities û and û₀ (equation 3). The form of equation 4 allowsfor an expansion of û_(S) in terms of {circumflex over (V)}û₀. Thisseries expansion can be done in different ways, e.g., according to theLippmann-Schwinger series or to the Bremmer coupling series. Theperturbation approach and these types of series expansions are useful indescribing scattering phenomena.

A convolution-type representation theorem may be derived from equation 1for general perturbed media. Throughout this paper, the discussion iscentered on theorems that relate unperturbed fields in State A withperturbed fields in State B. In this perturbation approach we setÂ_(A)=Â_(B)=Â, Â_(A,0)=Â_(B,0)=Â₀, {circumflex over (B)}_(A)={circumflexover (B)}_(B)={circumflex over (B)}, {circumflex over(B)}_(A,0)={circumflex over (B)}_(B,0)={circumflex over (B)}₀, andlikewise for v and v₀. Thus, from equation 1 we start with

∫_(v) [û _(A,0) ^(T) Kŝ _(b) −ŝ _(A) ^(T) Kû _(B) ]d ³ r=

û _(A,0) ^(T) {circumflex over (M)} ₁ ^(P) û _(B) d ² r+∫ _(v) û _(A,0)^(T) {circumflex over (M)} ₂ ^(P) û _(B) d ³ r;  (5)

where {circumflex over (M)}₁ ^(P)=K[N_(r)−Â₀(v₀·n)] and {circumflex over(M)}₂ ^(P)=K[Â(iω+v·∇)−Â₀(iω−v₀·∇)+{circumflex over (B)}−{circumflexover (B)}₀].

∫_(v) [û _(A,0) ^(T) Kŝ _(B) −ŝ _(A) ^(T) Kû _(B,0) ]d ³ r=

û _(A,0) ^(T) {circumflex over (M)} ₁ ⁰ û _(B,0) d ² r+∫ _(v) û _(A,0)^(T) {circumflex over (M)} ₂ ⁰ û _(B,0) d ³ r,  (6)

with {circumflex over (M)}₁ ⁰={circumflex over (M)}₁^(P)=K[N_(r)−Â₀(v₀·n)] and {circumflex over (M)}₂ ⁰=K[2Â₀(v₀·∇)]. Byusing the identity û=û₀+û_(S), and after inserting equation 6 in theleft-hand side of equation 5 we get

−∫_(v) ŝ _(A) ^(T) Kû _(B,S) d ³ r=

û _(A,0) ^(T) {circumflex over (M)} ₁ ^(P) û _(B,S) d ² r+∫ _(v) û_(A,0) ^(T) {circumflex over (M)} ₂ ^(P) û _(B,S) d ³ r+∫ _(v) û _(a,0)^(T) K{circumflex over (V)}û _(B,0) d ³ r  (7)

given that Δ{circumflex over (M)}₂={circumflex over (M)}₂^(P)−{circumflex over (M)}₂ ⁰=K{circumflex over (V)}. This equation is ageneralized convolution-type theorem that relates field perturbations atState B (left-hand side of the equation), with field perturbations andunperturbed fields in both States in the right-hand side.

The following step is to convert the reciprocity theorem in equation 7into a representation theorem by replacing the field quantities by theircorresponding Green's functions. The Green's matrices satisfy{circumflex over (L)}Ĝ=1δ(r′−r) and {circumflex over (L)}₀Ĝ₀=1δ(r′−r),with Ĝ⁻=Ĝ₀+Ĝ_(S). In this formulation waves in State A are described byĜ₀(r_(A), r), denoting the Green's matrix for the unperturbed impulseresponse observed at r_(A) due to an excitation at r (for brevity weomit the dependency on the frequency ω). Likewise waves in State B arerepresented by the perturbed Green's matrix Ĝ(r_(B), r). This gives

K′Ĝ _(S)(r _(B) ,r _(A))=

Ĝ ₀ ^(T)(r _(A) ,r){circumflex over (M)} ₁ ^(P) Ĝ _(S)(r _(B) ,r)d ² r+∫_(v) Ĝ ₀ ^(T)(r _(A) ,r){circumflex over (M)} ₂ ^(P) Ĝ _(B) ^(S)(r _(B),r)d ³ r. +∫ _(v) Ĝ ₀ ^(T)(r _(A) ,r)K{circumflex over (V)}Ĝ _(B) ⁰(r_(B) ,r)d ³ r,  (8)

where K′=−K. Equation 8 is important for the description of fieldperturbations for many physical systems. To illustrate this, let usconsider a special case: that of fields in nonmoving media (i.e.,v=v₀=0), or when v=−v₀. In either case, equation 8 simplifies to

K′Ĝ _(S)(r _(B) ,r _(A))=

Ĝ ₀ ^(T)(r _(A) ,r){circumflex over (M)} ₁ ^(P) Ĝ _(S)(r _(B) ,r)d ² r+∫_(v) Ĝ ₀ ^(T)(r _(A) ,r)K{circumflex over (V)}Ĝ _(B)(r _(B) ,r)d ³r.  (9)

Equation 9 is a generalized version of Green's Theorem as it is usuallypresented in the physical description of many different physicalphenomena. It shows that the Green's matrix for the field perturbationsobserved r_(B) can be reconstructed by convolutions of unperturbedfields observed at r_(A) with unperturbed fields and field perturbationsobserved at r_(B). The boundary integral vanishes when i) homogeneousboundary conditions are imposed on ∂v or ii) when the boundary tends toinfinity and one or more of the loss matrices {circumflex over (B)},{circumflex over (B)}₀, Jm{Â} or Jm{Â₀} are finite within the support ofv (i.e., when fields are quiescent at infinity). In either case,equation 9 gives

K′Ĝ _(S)(r _(B) ,r _(A))=∫_(v) Ĝ ₀ ^(T)(r _(A) ,r)K{circumflex over(V)}Ĝ(r _(B) , r)d ³ r.  (10)

This equation is a general matrix-vector form of the Lippmann-Schwingerintegral, yielding field perturbations for any physical phenomenadescribed by equation 3. Along with series expansions for fieldperturbations that follow from equation 4, equations 8 and 10 describescattering phenomena.

Correlation-type representation theorems may be derived for perturbedmedia, based on the more general theorems. We begin, in analogy to theprevious derivation, by rewriting equation 2 to relate unperturbedfields in State A with perturbed fields in State B, with the followingexpression

∫_(v) [û _(A,0) ^(†) ŝ _(B) +ŝ _(A) ^(†) û _(B) ]d ³ r=

û _(A,0) ^(†) {circumflex over (M)} ₃ ^(P) û _(B) d ² r+∫ _(v) û _(A,0)^(†) {circumflex over (M)} ₄ ^(P) û _(B) d ³ r;  (11)

where the matrices {circumflex over (M)}₃ ^(P) and {circumflex over(M)}₄ ^(P) are given by {circumflex over (M)}₃ ^(P)=N_(r)−Â₀ ^(†)(v₀·n)and {circumflex over (M)}₄ ^(P)=Â(iω+v·∇)−Â₀ ^(†)(iω+v₀·∇ )+{circumflexover (B)}+{circumflex over (B)}₀ ^(†) . Also analogously to thederivation in the previous section, we consider a correlation-typetheorems relating unperturbed fields in both States from equation 1,given by

∫_(v) [û _(A,0) ^(†) ŝ _(B) +ŝ _(A) ^(†) û _(B,0) ]d ³ r=

û _(A,0) ^(†) {circumflex over (M)} ₃ ⁰ û _(B,0) d ² r+∫ _(v) û _(A,0)^(†) {circumflex over (M)} ₄ ⁰ û _(B,0) d ³ r,  (12)

with {circumflex over (M)}₃ ⁰={circumflex over (M)}₃ ^(P)=N_(r)−Â₀^(†)(v₀·n) and {circumflex over (M)}₄ ⁰=Â₀(iω+v·∇)−Â₀^(†)(iω+v₀·∇)+{circumflex over (B)}₀+{circumflex over (B)}₀ ^(†). Giventhat {circumflex over (M)}₄ ^(P)−{circumflex over (M)}₄ ⁰={circumflexover (V)}⁻ and û=û₀+û̂_(s), then by inserting equation 12 in theleft-hand side of equation 11 gives

∫_(v) ŝ _(A) ^(†) û _(B,S) d ³ r=

û _(A,0) ^(†) {circumflex over (M)} ₃ ^(P) û _(B,s) d ² r+∫ _(v) û_(A,0) ^(†) {circumflex over (M)} ₄ ^(P) û _(B,S) d ³ r+∫ _(v) û _(A,0)^(†) {circumflex over (V)}û _(B,0) d ³ r  (13)

This is a generalized correlation-type theorem that relates fieldperturbations at State B (left-hand side of the equation) unperturbedand perturbed fields on both States (right-hand side). Note that, as inthe convolution theorem in equation 7, the surface integral containsunperturbed fields from State A and field perturbations from State B.With the same Green's matrix representation used in deriving equation 9,equation 13 can be written as

Ĝ _(S)(r _(B) ,r _(A))=

Ĝ ₀ ^(†)(r _(A) ,r){circumflex over (M)} ₃ ^(P) Ĝ _(S)(r _(B) ,r)d ² r+∫_(v) Ĝ ₀ ^(†)(r _(A) ,r){circumflex over (M)} ₄ ^(P) Ĝ _(S)(r _(B) ,r)d³ r+∫ _(v) Ĝ ₀ ⁵⁵⁴ (r _(A) ,r){circumflex over (V)}{circumflex over(G)}₀(r _(B) , r)d ³ r.  (14)

This correlation-type representation theorem describes how the fieldperturbations sensed at r_(B) due to a source at r_(A) can be retrievedfrom cross correlations between unperturbed fields sensed at r_(A) withunperturbed fields and field perturbations observed at r_(B). Equation14 relates to the general formulations proposed by Wapenaar et al.(2006) and Snieder et al. (2007). In the formulation by Wapenaar et al.and Snieder et al., the reconstruction of the Green's functions bycross-correlations retrieves the causal and anticausal unperturbedresponses Ĝ₀(r_(B),r_(A)) or Ĝ₀ ^(†)(r_(B),r_(A)), or the perturbed onesĜ(r_(B),r_(A)). or Ĝ^(†)(r_(B),r_(A)). Here, the theorem in equation 14(as well as in equation 9) retrieves only the causal field perturbationmatrix Ĝ_(S)(r_(B),r_(A)). Because the theorems of Wapenaar et al. andSnieder et al. retrieve both causal and anticausal responses, we referto them herein as two-sided theorems; while equation 14 is a one-sidedtheorem because it only yields a causal response. In general, the volumeintegrals in equation 14 cannot be neglected, so the responseĜ_(S)(r_(B),r_(A)) cannot typically be extracted only from the surfaceintegral.

Reconstructing the Scattered Field Response

Monitoring parameter changes from volume sources. Although in generalthe correlation theorem in equation 14 is not suitable for the practiceof “remote sensing without a source”, there are two important specialcases that do allow for the retrieval of the medium's response fromobserved fields. Let us consider first the case of a nonmoving medium(v=v₀=0) when the boundary integral in equation 14 vanishes (seenecessary conditions in the derivation of equation 10). In that case,and given that {circumflex over (M)}₄ ^(P)={circumflex over (M)}₄0+{circumflex over (V)}, equation 14 becomes

Ĝ _(S)(r _(B) ,r _(A))=∫_(v) Ĝ ₀ ^(†)(r _(A) ,r){circumflex over (M)} ₄⁰ Ĝ _(S)(r _(B) ,r)d ² r+∫ _(v) Ĝ ₀ ^(†)(r _(A) ,r){circumflex over(V)}Ĝ(r _(B) ,r)d ³ r.  (15)

Now since {circumflex over (M)}₄ ⁰=Jm{Â)}+{circumflex over(B)}₀+{circumflex over (B)}₀ ^(\), the first integral in equation 15accounts only for energy dissipation in the background medium. Hence,when the background loss parameters (represented by the matrix{circumflex over (M)}₄ ⁰ are negligible compared to the changes{circumflex over (V)}, the first integral in equation 15 can be ignoredleaving

Ĝ _(S)(r _(B) ,r _(A))=∫_(v) Ĝ ₀ ^(†)(r _(A) ,r){circumflex over (V)}Ĝ(r_(B) ,r)d ³ r.  (16)

Note that this integral is remarkably similar to the generalizedLippmann-Schwinger integral in equation 10, with Ĝ₀(r_(A),r) replaced by⁻Ĝ₀ ^(†)(r_(A),r)⁻ in the integrand. We shall explore this similaritylater in our discussion. Next, we consider volume noise sources{circumflex over (σ)}(r,ω) distributed within V. For any two such noisesources, their respective vector elements {circumflex over (σ)}_(i)(r,ω)and {circumflex over (σ)}_(j)(r′,ω′) are uncorrelated for any i≠j andr≠r′; while their power spectrum is the same for any r and source-vectorcomponents, apart from frequency- and space-varying excitationfunctions. The uncorrelated noise sources obey the relation

{circumflex over (σ)}(r){circumflex over (σ)}^(†)(r′)

=||{circumflex over (N)}||²{circumflex over (Σ)}{circumflex over(V)}(r)δ(r−r′), where the right-hand side is a spatial ensemble average,||{circumflex over (N)}||² is the noise power spectrum and the diagonalmatrix {circumflex over (Σ)} contains the excitation functions. Thepresence of {circumflex over (V)} in the ensemble average aboveindicates that the perturbed-state volume sourcest {circumflex over(σ)}(r,ω) are locally proportional to the medium parameter changes at r.Under these conditions, the spatial averaging of the measured responsesû^(obs)(r) is

(û ^(obs)(r _(B)){û ₀ ^(obs)(r _(A))}^(†))=∫_(v) ||{circumflex over(N)}|| ² Ĝ ₀ ^(†)(r _(A) ,r){circumflex over (Σ)}{circumflex over(V)}Ĝ(r _(B) ,r)d ³ r.  (17)

Using this result together with that in equation 16 gives

Ĝ _(S)(r _(B) ,r _(A)){circumflex over (N)}=(û ^(obs)(r _(B)){û ₀^(obs)(r _(A))}^(†)).  (18)

For cases where equation 16 is valid, equation 18 states that one canobtain the scattered field response between the observation points atr_(A) and r_(B) by cross correlations of ambient noise records used inevaluating (û^(obs)(r_(B)){û₀ ^(obs)(r_(A))}^(†)). What sets this resultapart from previous results for generalized representation theorems isthat here the random volume noise sources are locally proportional tothe medium parameter perturbation, e.g., observed signals can be thoughtof as being caused by changes in the medium. This interpretation of thegeneral result in equation 18 is closely connected with the concept ofcoda-wave interferometry. Coda-wave theory relies on a energypropagation regime where the volume scatterers (i.e., the mediumperturbations here described by the spatially-varying matrix {circumflexover (V)}) behave as secondary sources emitting waves that sample andaverage the medium multiple times. In the practice of coda-waveinterferometry, cross-correlations of the late portions of the observeddata (which represent waves in the multiple scattering regime) provide ameasure of the medium perturbations and can be used to monitor changesin the medium. The result in equation 18 is related to that of coda-waveinterferometry because the excitation is provided by volume sources thatare proportional to the medium perturbation (i.e., to the localscattering strength), and the cross-correlations of the data observed atthe two observation points yields an estimate of the scattered fieldimpulse response between the two receivers. While coda-waveinterferometry is typically accomplished by single receiver measurements(where r_(A)=r_(B)), equation 18 demonstrates that thecross-correlations of the responses sensed at two or more receivers canalso extract information about scatterers and/or changes in the medium.Furthermore, the result in equation 18 applies not just to waves inlossless materials (e.g., acoustic and elastic); it also holds fordissipative acoustic, elastic and electromagnetic phenomena,quantum-mechanical waves, mass, heat or advective transport systems,etc. Therefore, the concept of monitoring medium perturbationsintroduced by coda-wave interferometry in fact applies to experimentswith multiple observation points and all physical systems where equation16 holds.

Reconstructing Perturbations from the Surface Integral

Another important special case for equation 14 occurs in the context ofretrieving the Green's matrix of field perturbations bycross-correlations. Setting the loss matrices. {circumflex over(B)}={circumflex over (B)}₀ ⁻=Jm{Â₀}=Jm{Â₀}= 0, equation 14 yields

Ĝ _(S)(r _(B) ,r _(A))=

Ĝ ₀ ^(†)(r _(A) ,r){circumflex over (N)} _(r) Ĝ _(S)(r _(B) ,r)d ² r+∫_(v) Ĝ ₀ ^(†)(r _(A) ,r){circumflex over (V)}Ĝ(r _(B) ,r)d ³ r;  (19)

where {circumflex over (M)}₄ ^(P)={circumflex over (V)}. Since equation19 holds when all loss matrices are set to zero, it is strictly validfor systems that are invariant under time-reversal. Thus, equation 19retrieves the field perturbations Ĝ_(S) ⁻(r_(B),r_(A)) for losslessacoustic and elastic wave propagation, for electromagnetic phenomena inhighly resistive media, and for the Schrödinger equation, for example.Next, we consider a medium configuration as in FIG. 2, where {circumflexover (V)}≠0 only for r εsup

and the observation points are away from

. In this configuration, there are sources r₁ ε∂V₁ (where ∂V₁ is acontinuous segment of ∂V) for which the stationary paths of thedirect-trasmitted unperturbed waves are not affected by the mediumperturbations in

. This is depicted in FIG. 2 a. Because the unperturbed waves do notcross

, the leading order stationary phase contribution of Ĝ₀^(†)(r_(A),r){circumflex over ( VĜ₀(r_(B),r) to the volume integral inequation 19 is negligible because {circumflex over (V)}=0 along thestationary unperturbed-wave paths.

While the remaining contribution of the volume integral (given by Ĝ₀^(†)(r_(Z),r){circumflex over (V)}Ĝ_(S)(r_(b),r) in the integrand) isnot negligible, its contribution (to leading order in the scatteredfields) has the same phase of that of the surface integral since theintegrands also have the same phase. Therefore, it is possible toestimate the scattered field response according to

Ĝ _(S)(r _(B) ,r _(A))≈∫_(∂V) ₁ Ĝ ₀ ^(†)(r _(A) ,r){circumflex over (N)}_(r) Ĝ _(S)(r _(B) ,r)d ² r.  (20)

Evaluating solely the surface integral according to equation 20 shouldthen retrieve Ĝ_(S)(r_(B),r_(A)) with correct phase spectra, but theamplitude spectra might be distorted by ignoring the volume integral inequation 19. Note also that the result in equation 20 is not valid forall sources in the closed surface ∂V. When ∂V₁ is an infinite plane, andthe wave propagation regimes can be described by coupled one-wayoperators, the result in equation 20 is exact: the out-going scatteredwaves propagating between receivers are obtained by cross-correlationsof the scattered fields observed at ∂V₁ with the measured in-goingtransmitted waves. The result in equation 20 can be used to retrieveĜ_(S)(r_(B),r_(A)) from remote sources on ∂V₁. Here the terms out- andin-going waves to denote propagation direction with respect to theposition of target scatterers; i.e., in-going waves propagate toward thescatterers, whereas back-scattered waves are out-going.

Referring now to FIGS. 14 and 15 and with the benefit of theabove-described geophysical information gathering system 100 andinterferometry techniques, methods for gathering geophysical informationwill be described. Referring to FIG. 14, a method 1400 according to oneor more embodiments includes 1402 receiving an electromagnetic field attwo or more receivers, 1404 generating a pseudo-source using thereceived electromagnetic fields, and 1406 estimating a reservoirparameter using the pseudo-source. The term pseduo-source as used hereinrefers to a suite of geophysical information generated from returninformation received at a plurality of receivers, where the generatedinformation represents a physical source of known characteristicslocated at a receiver location. The received electromagnetic field maybe the result of a physical source field interacting with a subsurfacetarget, or the received field may be the result of naturalelectromagnetic radiation, such as from the sun, penetrating the earthand interacting with the subsurface target.

FIG. 15 illustrates an iterative method 1500 that includes 1502generating an electromagnetic source field and 1504 recording a returnelectromagnetic field at two or more receivers. The method 1500 furtherincludes 1506 generating an Earth model, 1508 generating apseudo-source, and 1510 determining whether the Earth model andpseudo-source are consistent. In this method, the Earth model consistsof one- or multi-dimensional representations of the subsurfacestructure. In one embodiment, the representations may be two- orthree-dimensional representations, in any form, of any quantitative orqualitative forms of spatial parameter distributions of relevantphysical properties of the subsurface materials. Relevant physicalproperties of the subsurface materials may include, for example:acoustic, elastodynamic, electric, electromagnetic, seismo-electric,thermal, or mass properties. Where there is consistency between thepseudo-source and the Earth model 1510, reservoir parameters may beestimated 1514, otherwise 1512 the Earth model is updated and a newpseudo-source is generated 1508. A final Earth model can be obtained viathe method described in regard to FIG. 15 by setting chosen quantitativethresholds for measuring consistency between the acquired data and thedata predicted based on the current Earth model. Additionally, theinference of a final Earth model through an iterative method may alsodraw upon any other types of additional subsurface information, e.g.,seismic data and/or images, borehole geophysical information, or anyother type of geophysical data.

While a single pseudo-source record for a given radiator location can begenerated from a minimum of two receivers, it is also possible togenerate pseudo-source data from all possible receiver combinations froma plurality of receivers distributed over a chosen survey area.Increasing the number of receivers for which pseudo-source data isgenerated increases the overall volume of pseudo-source data and canprovide additional information about the target subsurface structuresand their physical properties.

The methods as described above may be conducted whether or not physicalsource parameters are known. Electromagnetic interferometry techniquesaccording to one or more embodiments may include using interferometry toprocess information in the form of data signals generated by poorlyknown and/or controlled physical sources to generate pseudo-sources atthe receiver locations, where the pseduo-sources have precisely-knownparameters. The pseudo-sources can then be used to extract more completeand reliable information about the Earth's subsurface. Severalembodiments may use aspects of the general theory discussed above toobtain the desired results from interferometry. We shall consider twoexamples, which lead to two different data processing routines.

EXAMPLE 1

In this example, sources and receivers may be densely sampled, and boththe vertical electric and magnetic fields are reliably measured. Themethod includes using electric and magnetic fields recorded at receiversx_(A) and x to separate the upward decaying fields in {circumflex over(P)}⁻(x_(A),x_(S)) from the downward decaying fields in {circumflex over(P)}⁺(x,x_(S)). Where {circumflex over (P)}⁻ and {circumflex over (P)}⁺are flux-normalized up-going and down-going vector fields, respectively.The method further includes solving the inverse integral equation for{circumflex over (R)}₀ ⁺(x_(A),x), where {circumflex over (R)}₀ ⁺ is theFourier transform of an impulse response, from the input data{circumflex over (P)}⁻(x_(A),x_(S)) and {circumflex over (P)}⁺(x,x_(S)).Then, we may use {circumflex over (R)}₀ ⁺(x_(A),x) (which is thepseudo-source response) to estimate subsurface information.

EXAMPLE 2

In this example, the receivers are coarsely sampled, and/or theseparation of up- from down-decaying fields is not feasible, i.e.,vertical fields cannot be measured or data are unreliable. A methodsuitable for these conditions includes establishing a prior backgroundmodel describing electromagnetic properties of sea water and air, or usea best-fit subsurface model from standard processing of CSEM data. Themethod further includes numerically modeling fields Ĝ₀(r_(A),r) andĜ₀(r_(B),r) to simulate background response acquired by receivers atr_(A) and r_(B). The method includes matching Ĝ₀(r_(A,B),r) to thefull-field acquired data û(r_(A,B),r) by adaptive subtraction and obtainû₀(r_(A,B),r) and û_(S)(r_(A,B),r) as by-product.

One may then evaluate equation 14 above to estimate pseudo-sourceresponse Ĝ_(S)(r_(B),r_(A)). The surface integral is computed from thedata û₀(r_(A,B),r) and û_(S)(r_(A,B),r). The Green's function kernel canbe computed via matrix-vector field deconvolutions. The volume integralsare evaluated numerically by setting the zero-order scatteringapproximation Ĝ_(S)→Ĝ₀; the matrix {circumflex over (M)}₄ ⁰ is computedfrom the background model, and {circumflex over (V)} is extracted fom aprior Earth model, which may come from standard CSEM processing, or fromprevious iterations of this processing routine.

In one or more embodiments, one may then use the estimated pseudo-sourceresponse Ĝ_(S)(r_(B),r_(A)) to infer or estimate subsurface properties.Where the estimated Earth model properties are not consistent with theoriginally acquired data, one may then iterate the above evaluation toestimate Ĝ_(S)(r_(B),r_(A)) and estimate the subsurface properties untilreaching an acceptable Earth model that is within a predeterminedthreshold. An “acceptable” Earth model can be defined by some form ofqualitative and/or quantitative measure of the differences between theacquired data and the data that would be predicted based on the currentEarth model. In addition, the criteria for acceptable Earth models mayalso rely on other geophysical or geological information, e.g., maps,borehole data, seismic profiles, seismic images, gravity data, orresistivity profiles.

The methods of the present disclosure may be performed usingelectromagnetic information or in combination with any other usefulgeophysical information. For example, estimating parameters 406, 1514may include the use of seismic information gathered before, concurrentlywith or after gathering the electromagnetic information. In one or moreembodiments, other geophysical information such as seismic informationmay be used to generate, constrain, or otherwise clarify the Earth model1506.

The present disclosure is to be taken as illustrative rather than aslimiting the scope or nature of the claims below. Numerous modificationsand variations will become apparent to those skilled in the art afterstudying the disclosure, including use of equivalent functional and/orstructural substitutes for elements described herein, use of equivalentfunctional couplings for couplings described herein, and/or use ofequivalent functional actions for actions described herein. Suchinsubstantial variations are to be considered within the scope of theclaims below.

Given the above disclosure of general concepts and specific embodiments,the scope of protection is defined by the claims appended hereto. Theissued claims are not to be taken as limiting Applicant's right to claimdisclosed, but not yet literally claimed subject matter by way of one ormore further applications including those filed pursuant to the laws ofthe United States and/or international treaty.

1. A method for gathering geophysical information comprising: receivingelectromagnetic energy emanating from a target using a plurality ofreceivers; and generating a pseudo-source based at least in part on alocation of one or more of the plurality of receivers and the receivedelectromagnetic energy.
 2. A method according to claim 1, wherein theact of receiving electromagnetic energy comprises receivingmulti-component electromagnetic energy.
 3. A method according to claim2, wherein the multi-component electromagnetic energy comprises: one ormore magnetic components, one or more electrical components, or acombination thereof.
 4. A method according to claim 1, wherein theplurality of receivers comprises: one or more receivers located on land,in a marine environment, or in an area that includes both a land portionand a marine portion.
 5. A method according to claim 1, wherein the actof generating a pseudo-source further comprises using acomputer-generated set of parameters.
 6. A method according to claim 5,wherein the generated set of parameters emulate a physical source havingknown parameters, and wherein the emulated physical source is located ator near the location of one of the receivers.
 7. A method according toclaim 1 further comprising the act of: transmitting electromagneticenergy from a physical source, wherein the electromagnetic energyemanating from the target is responsive to the transmittedelectromagnetic energy.
 8. A method according to claim 7, wherein thephysical source comprises a multi-dimensional structure that generatesmulti-component electromagnetic energy fields.
 9. A method according toclaim 8, wherein the act of transmitting the electromagnetic energyfurther comprises transmitting a multi-component electromagnetic energyfield.
 10. A method according to claim 1, further comprising the act of:generating an initial Earth model.
 11. A method according to claim 10,further comprising the act of: updating the Earth model based at leastin part on the generated pseudo-source.
 12. A method according to claim8, further comprising the act of: conveying the physical source, whereinthe conveying comprises conveying the physical source in a body ofwater, on land, in the air, underground, or any combination thereof. 13.A method according to claim 7, wherein the act of generating apseudo-source further comprises generating a set of parameters that areindependent of any parameter of the physical source.
 14. A methodaccording to claim 1, wherein the act of generating a pseudo-sourcefurther comprises generating pseudo-source parameters for each receiverin the plurality of receivers.
 15. A system for gathering geophysicalinformation comprising: a processor; a physical source configured totransmit electromagnetic energy; and a plurality of receivers configuredto receive electromagnetic energy emanating from a target; wherein theprocessor generates a pseudo-source based at least in part on a locationof one or more of the plurality of receivers and the receivedelectromagnetic energy.
 16. A system according to claim 15, wherein theplurality of receivers are further configured to receive multi-componentelectromagnetic energy.
 17. A system according to claim 16, wherein themulti-component electromagnetic energy includes one or more magneticcomponents, one or more electrical components, or a combination thereof.18. A system according to claim 15, wherein the plurality of receiversincludes one or more receivers located on land, in a marine environment,or in an area that includes both a land portion and a marine portion.19. A system according to claim 15, wherein the processor is furtherconfigured to generate a set of parameters representative of thepseudo-source.
 20. A system according to claim 19, wherein the generatedset of parameters emulate a physical source having known parameters, andwherein the emulated physical source is located at or near the locationof one of the receivers.
 21. A system according to claim 15, wherein theelectromagnetic energy emanating from the target is responsive to thetransmitted electromagnetic energy.
 22. A system according to claim 15,wherein the physical source comprises a multi-dimensional structure thatgenerates multi-component electromagnetic energy fields.
 23. A systemaccording to claim 22, wherein the physical source is further configuredto transmit a multi-component electromagnetic energy field.
 24. A systemaccording to claim 15, wherein the processor is further configured togenerate an initial Earth model.
 25. A system according to claim 24,wherein the processor is further configured to update the Earth modelbased at least in part on the generated pseudo-source.
 26. A systemaccording to claim 15, wherein the physical source is further configuredto be conveyed in a body of water, on land, in the air, underground, orany combination thereof.
 27. A system according to claim 15, wherein theprocessor is further configured to generate pseudo-source parametersthat are independent of any parameter of the physical source.
 28. Asystem according to claim 15, wherein the processor is furtherconfigured to generate pseudo-source parameters for each receiver in theplurality of receivers.
 29. A computer usable medium having a computerreadable program code embodied therein, wherein the computer readableprogram code is adapted to be executed to implement the method of claim1.